Minimal coefficients in Hölder conditions in the Wiener space
Author:
J. Yeh
Journal:
Proc. Amer. Math. Soc. 25 (1970), 385-390
MSC:
Primary 28.46
DOI:
https://doi.org/10.1090/S0002-9939-1970-0255762-4
MathSciNet review:
0255762
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Abstract | References | Similar Articles | Additional Information
Abstract: For almost every $x$ in the Wiener space ${C_w}$, the Hölder condition $|x(t’) - x(t'')| \leqq h|t’ - t''{|^\alpha }$ holds for some $h > 0$ when $\alpha \in (0,\tfrac {1} {2})$. Let ${\phi _\alpha }[x]$ be the infimum of all $h > 0$ for fixed $x$ and $\alpha$. In the present paper we prove that every positive power of ${\phi _\alpha }[x]$ is Wiener integrable over ${C_w}$ and give an estimate for the Wiener integral.
- I. M. Gel′fand and A. M. Yaglom, Integration in function spaces and its application to quantum physics, Uspehi Mat. Nauk (N.S.) 11 (1956), no. 1(67), 77–114 (Russian). MR 0078910
- Norbert Wiener, Generalized harmonic analysis, Acta Math. 55 (1930), no. 1, 117–258. MR 1555316, DOI https://doi.org/10.1007/BF02546511
- J. Yeh, Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc. 95 (1960), 433–450. MR 125433, DOI https://doi.org/10.1090/S0002-9947-1960-0125433-1
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Additional Information
Keywords:
Wiener measure,
Brownian motion,
continuity of sample paths,
Hölder condition,
essential boundedness
Article copyright:
© Copyright 1970
American Mathematical Society